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A168240 1+7*n+13*n^2. 3
21, 67, 139, 237, 361, 511, 687, 889, 1117, 1371, 1651, 1957, 2289, 2647, 3031, 3441, 3877, 4339, 4827, 5341, 5881, 6447, 7039, 7657, 8301, 8971, 9667, 10389, 11137, 11911, 12711, 13537, 14389, 15267, 16171, 17101, 18057, 19039, 20047, 21081, 22141, 23227 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients defined by f(x + n*f(x))/f(x). a(n) is the quotient at x=3.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

From R. J. Mathar, Nov 23 2009: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(21+4*x+x^2)/(1-x)^3. (End)

E.g.f.: (13*x^2 + 20*x + 1)*exp(x). - G. C. Greubel, Apr 09 2016

EXAMPLE

f(x)= 13 when x =3. Hence at n=1, f(x + f(x))/f(x) = 21 = a(1).

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {21, 67, 139}, 50] (* G. C. Greubel, Apr 09 2016 *)

Table[1+7n+13n^2, {n, 50}] (* Harvey P. Dale, Mar 22 2019 *)

PROG

(PARI) a(n)=1+7*n+13*n^2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A168235, A165806, A165808, A165809.

Sequence in context: A048713 A219814 A219379 * A123779 A123839 A180758

Adjacent sequences:  A168237 A168238 A168239 * A168241 A168242 A168243

KEYWORD

nonn,easy

AUTHOR

A.K. Devaraj, Nov 21 2009

EXTENSIONS

Edited, definition simplified, sequence extended beyond a(8) by R. J. Mathar, Nov 23 2009

STATUS

approved

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Last modified October 6 05:47 EDT 2022. Contains 357261 sequences. (Running on oeis4.)